Finite Group Databasebeta

← Group #229256

Character table — Group #229256

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888222244444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
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χ181-111-1-11-11-1-1-11-111iiii−i−i−i−i1111-1-1-1-111-1-11ii−i−i−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i−ii−ii1-1i−iii−i−i11-1-1-1-111-1-111-11-11−ii−ii
χ191-111-1-11-11-1-1-11-111iiii−i−i−i−i1111-1-1-1-1-1-1111−i−iiiii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−ii−ii−i-11−ii−i−iii-1-11111-1-111-1-1-11-11−ii−ii
χ201-111-1-11-11-1-1-11-111iiii−i−i−i−i1111-1-1-1-1-1-1111−i−iii−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i−ii−ii-11−ii−i−iii-1-111-1-111-1-1111-11-1i−ii−i
χ211-111-1-11-11-1-1-11-111iiii−i−i−i−i-1-1-1-1111111-1-11ii−i−iii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiiii−i−ii1-1i−i−i−iii-1-11111-1-1-1-1111-1-11i−i−ii
χ221-111-1-11-11-1-1-11-111iiii−i−i−i−i-1-1-1-1111111-1-11ii−i−i−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii−iii−i1-1i−i−i−iii-1-111-1-11111-1-1-111-1−iii−i
χ231-111-1-11-11-1-1-11-111iiii−i−i−i−i-1-1-1-11111-1-1111−i−iiiii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiiii−i−ii-11−iiii−i−i11-1-111-1-1-1-111-111-1−iii−i
χ241-111-1-11-11-1-1-11-111iiii−i−i−i−i-1-1-1-11111-1-1111−i−iii−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii−iii−i-11−iiii−i−i11-1-1-1-11111-1-11-1-11i−i−ii
χ251-111-1-11-11-1-1-11-111−i−i−i−iiiii1111-1-1-1-111-1-11−i−iiiii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiiii−ii−i1-1−ii−i−iii11-1-1-1-111-1-111-11-11i−ii−i
χ261-111-1-11-11-1-1-11-111−i−i−i−iiiii1111-1-1-1-111-1-11−i−iii−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii−ii−ii1-1−ii−i−iii11-1-111-1-111-1-11-11-1−ii−ii
χ271-111-1-11-11-1-1-11-111−i−i−i−iiiii1111-1-1-1-1-1-1111ii−i−iii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiiii−ii−i-11i−iii−i−i-1-111-1-111-1-1111-11-1−ii−ii
χ281-111-1-11-11-1-1-11-111−i−i−i−iiiii1111-1-1-1-1-1-1111ii−i−i−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii−ii−ii-11i−iii−i−i-1-11111-1-111-1-1-11-11i−ii−i
χ291-111-1-11-11-1-1-11-111−i−i−i−iiiii-1-1-1-1111111-1-11−i−iiiii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−ii−i−ii1-1−iiii−i−i-1-111-1-11111-1-1-111-1i−i−ii
χ301-111-1-11-11-1-1-11-111−i−i−i−iiiii-1-1-1-1111111-1-11−i−iii−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i−iii−i1-1−iiii−i−i-1-11111-1-1-1-1111-1-11−iii−i
χ311-111-1-11-11-1-1-11-111−i−i−i−iiiii-1-1-1-11111-1-1111ii−i−iii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−ii−i−ii-11i−i−i−iii11-1-1-1-11111-1-11-1-11−iii−i
χ321-111-1-11-11-1-1-11-111−i−i−i−iiiii-1-1-1-11111-1-1111ii−i−i−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i−iii−i-11i−i−i−iii11-1-111-1-1-1-111-111-1i−i−ii
χ33222222222-222-2-2-2222222222000000002222-2222200000000-2-2-2-2-20000000000000000-2-2-2-2000000000000000000000000
χ34222222222-222-2-2-222222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000000002222000000000000000000000000
χ35222222222-222-2-2-22-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200000000-222220000000000000000-2-222000000000000000000000000
χ36222222222-222-2-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000000022-2-2000000000000000000000000
χ3722222222-22-2-2222-200000000222222220000-2000022222222-20000-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ3822222222-22-2-2222-200000000222222220000-20000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000022220000000000000000000000000000
χ3922222222-22-2-2222-200000000-2-2-2-2-2-2-2-20000-200002222-2-2-2-2-20000222200000000-2-2220000000000000000000000000000
χ4022222222-22-2-2222-200000000-2-2-2-2-2-2-2-20000-20000-2-2-2-22222-2000022220000000022-2-20000000000000000000000000000
χ41222-22-2-2-2202-2000-222-2-222-2-222−2−222−2−22-22-202-22-200000000000002−22−222−2−222−2−2000000002−22−22−22−20000000000000000
χ42222-22-2-2-2202-2000-222-2-222-2-222−2−222−2−2-22-220-22-2200000000000002−22−222−2−222−2−200000000−22−22−22−220000000000000000
χ43222-22-2-2-2202-2000-222-2-222-2-2−2−222−2−2222-22-202-22-20000000000000−22−22−2−222−2−22200000000−22−22−22−220000000000000000
χ44222-22-2-2-2202-2000-222-2-222-2-2−2−222−2−222-22-220-22-220000000000000−22−22−2−222−2−222000000002−22−22−22−20000000000000000
χ45222-22-2-2-2202-2000-2-2-222-2-22222−2−222−2−22-22-20-22-2200000000000002−22−2−2−222−2−22200000000−22−222−22−20000000000000000
χ46222-22-2-2-2202-2000-2-2-222-2-22222−2−222−2−2-22-2202-22-200000000000002−22−2−2−222−2−222000000002−22−2−22−220000000000000000
χ47222-22-2-2-2202-2000-2-2-222-2-222−2−222−2−2222-22-20-22-220000000000000−22−2222−2−222−2−2000000002−22−2−22−220000000000000000
χ48222-22-2-2-2202-2000-2-2-222-2-222−2−222−2−222-22-2202-22-20000000000000−22−2222−2−222−2−200000000−22−222−22−20000000000000000
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χ762-2-2-22-2220-200-22202−22−2−22−22-22-222-22-2000000000-222-22-2-2202−2−220000−22−222−22−20000000000000000−222−22−2−2200000000
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χ782-2-2-22-2220-200-2220−22−222−22−22-22-2-22-22000000000-222-2-222-20−222−20000−22−222−22−200000000000000002−2−222−2−2200000000
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χ802-2-2-22-2220-200-2220−22−222−22−2-22-222-22-2000000000-222-22-2-220−222−200002−22−2−22−2200000000000000002−2−22−222−200000000
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χ944-4-4444-4-40000000022−22−2222−222222−22−222222−2222−22−222200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ954-4-4444-4-400000000−222222−2222−22−222222−22−2222−222222−2200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ964-4-4444-4-400000000−222222−2222−22−2222−222222−2222−22−2222000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ974-4-4-44-44404004-4-4022−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ984-4-4-44-44404004-4-40−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).